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Journal Cover Physica D: Nonlinear Phenomena
  [SJR: 1.049]   [H-I: 102]   [3 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0167-2789
   Published by Elsevier Homepage  [3043 journals]
  • Identification of particle-laden flow features from wavelet decomposition
    • Authors: A. Jackson; B. Turnbull
      Abstract: Publication date: Available online 10 October 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): A. Jackson, B. Turnbull
      A wavelet decomposition based technique is applied to air pressure data obtained from laboratory-scale powder snow avalanches. This technique is shown to be a powerful tool for identifying both repeatable and chaotic features at any frequency within the signal. Additionally, this technique is demonstrated to be a robust method for the removal of noise from the signal as well as being capable of removing other contaminants from the signal. Whilst powder snow avalanches are the focus of the experiments analysed here, the features identified can provide insight to other particle-laden gravity currents and the technique described is applicable to a wide variety of experimental signals.

      PubDate: 2017-10-11T18:08:12Z
      DOI: 10.1016/j.physd.2017.09.009
  • Hyperbolic relaxation of the 2D Navier–Stokes equations in a bounded
    • Authors: Alexei Ilyin; Yuri Rykov; Sergey Zelik
      Abstract: Publication date: Available online 7 October 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Alexei Ilyin, Yuri Rykov, Sergey Zelik
      A hyperbolic relaxation of the classical Navier–Stokes problem in 2D bounded domain with Dirichlet boundary conditions is considered. It is proved that this relaxed problem possesses a global strong solution if the relaxation parameter is small and the appropriate norm of the initial data is not very large. Moreover, the dissipativity of such solutions is established and the singular limit as the relaxation parameter tends to zero is studied.

      PubDate: 2017-10-11T18:08:12Z
      DOI: 10.1016/j.physd.2017.09.008
  • Improving the Jacobian free Newton-Krylov method for the viscous-plastic
           sea ice momentum equation
    • Authors: Clint Seinen; Boualem Khouider
      Abstract: Publication date: Available online 4 October 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Clint Seinen, Boualem Khouider
      Sea ice plays a central role in regulating Earth’s radiative budget because of its high albedo effect, and its melting level during the summer season is considered to be an important index of global warming. Contemporary earth system models (ESM) utilize complex dynamical models for the pack ice to account for the variations of sea ice cover and its feedback on the earth system. There is a wide consensus in the climate modeling community that the ice pack is most accurately modeled as a viscous-plastic flow with a highly nonlinear rheology consisting of an elliptic-yield-curve constitutive law. However, sea ice dynamics remains one of the most uncertain factors in the ESM’s ability to address the climate change problem. The difficulty in accurately and efficiently solving numerically the associated highly nonlinear partial differential equations is believed to be a big contributor to this uncertainty. This work builds on recent efforts to construct fast and accurate numerical schemes for the viscous-plastic sea ice equations, based on a Jacobian free Newton Krylov (JFNK) algorithm. Here, we propose to improve on the JFNK approach by using a fully second order Crank–Nicolson-type method to discretize the sea ice momentum equations (SIME) instead of the previously used first order backward Euler. More importantly, we improve on the Jacobian free approximation by expressing the derivatives of the least cumbersome and linear terms in the discretized SIME functional in closed form and use a second order Gateaux-derivative approximation for the remaining terms, instead of using a first order approximation of the Gateaux derivative for the whole Jacobian matrix. Numerical tests performed on a synthetic exact solution for an augmented set of equations demonstrated that the new scheme is indeed second order accurate and the second order approximation of the Jacobian matrix was revealed to be crucial for the convergence of the nonlinear solver. One of the main difficulties in the JFNK approach resides in deciding on a stopping criterion for the Newton iterations. Our tests show that iterating beyond a certain level can in fact deteriorate the solution and prevent convergence. To overcome this issue, we suggest to use a conditional termination strategy by stopping the iterations as soon as the residual starts to increase. The resulting gain in efficiency overshadows any gains in accuracy when requiring formal convergence.

      PubDate: 2017-10-04T18:03:37Z
  • Local and global strong solutions for SQG in bounded domains
    • Authors: Peter Constantin; Huy Quang Nguyen
      Abstract: Publication date: Available online 21 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Peter Constantin, Huy Quang Nguyen
      We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of R 2 . When fractional Dirichlet Laplacian dissipation is added, global existence of strong solutions is obtained for small data for critical and supercritical cases. Global existence of strong solutions with arbitrary data is obtained in the subcritical cases.

      PubDate: 2017-09-26T17:33:44Z
      DOI: 10.1016/j.physd.2017.08.008
  • Eulerian dynamics with a commutator forcing III. Fractional diffusion of
           order 0<α<1
    • Authors: Roman Shvydkoy; Eitan Tadmor
      Abstract: Publication date: Available online 21 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Roman Shvydkoy, Eitan Tadmor
      We continue our study of hydrodynamic models of self-organized evolution of agents with singular interaction kernel ϕ ( x ) = x − ( 1 + α ) . Following our works Shvydkoy and Tadmor (2017) and Shvydkoy and Tadmor (in press) which focused on the range 1 ≤ α < 2 , and Do et al. (2017) which covered the range 0 < α < 1 , in this paper we revisit the latter case and give a short(-er) proof of global in time existence of smooth solutions, together with a full description of their long time dynamics. Specifically, we prove that starting from any initial condition in ( ρ 0 , u 0 ) ∈ H 2 + α × H 3 , the solution approaches exponentially fast to a flocking state solution consisting of a wave ρ ̄ = ρ ∞ ( x − t u ̄ ) traveling with a constant velocity determined by the conserved average velocity u ̄ . The convergence is accompanied by exponential decay of all higher order derivatives of u .

      PubDate: 2017-09-26T17:33:44Z
      DOI: 10.1016/j.physd.2017.09.003
  • Semi-global persistence and stability for a class of forced discrete-time
           population models
    • Authors: Daniel Franco; Chris Guiver; Hartmut Logemann; Juan Perán
      Abstract: Publication date: Available online 31 August 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Daniel Franco, Chris Guiver, Hartmut Logemann, Juan Perán
      We consider persistence and stability properties for a class of forced discrete-time difference equations with three defining properties: the solution is constrained to evolve in the non-negative orthant, the forcing acts multiplicatively, and the dynamics are described by so-called Lur’e systems, containing both linear and non-linear terms. Many discrete-time biological models encountered in the literature may be expressed in the form of a Lur’e system and, in this context, the multiplicative forcing may correspond to harvesting, culling or time-varying (such as seasonal) vital rates or environmental conditions. Drawing upon techniques from systems and control theory, and assuming that the forcing is bounded, we provide conditions under which persistence occurs and, further, that a unique non-zero equilibrium is stable with respect to the forcing in a sense which is reminiscent of input-to-state stability, a concept well-known in nonlinear control theory. The theoretical results are illustrated with several examples. In particular, we discuss how our results relate to previous literature on stabilization of chaotic systems by so-called proportional feedback control.

      PubDate: 2017-09-26T17:33:44Z
      DOI: 10.1016/j.physd.2017.08.001
  • Operator splitting method for simulation of dynamic flows in natural gas
           pipeline networks
    • Authors: Sergey A. Dyachenko; Anatoly Zlotnik; Alexander O. Korotkevich; Michael Chertkov
      Abstract: Publication date: Available online 19 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Sergey A. Dyachenko, Anatoly Zlotnik, Alexander O. Korotkevich, Michael Chertkov
      We develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme is unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.

      PubDate: 2017-09-20T17:10:15Z
      DOI: 10.1016/j.physd.2017.09.002
  • Phase models and clustering in networks of oscillators with delayed
    • Authors: Sue Ann Campbell; Zhen Wang
      Abstract: Publication date: Available online 19 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Sue Ann Campbell, Zhen Wang
      We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to determine model independent existence and stability results for symmetric cluster solutions. Our results extend previous work to systems with time delay and a more general coupling matrix. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies.

      PubDate: 2017-09-20T17:10:15Z
      DOI: 10.1016/j.physd.2017.09.004
  • 4-wave dynamics in kinetic wave turbulence
    • Authors: Sergio Chibbaro; Giovanni Dematteis; Lamberto Rondoni
      Abstract: Publication date: Available online 18 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Sergio Chibbaro, Giovanni Dematteis, Lamberto Rondoni
      A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an “interaction representation” and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z . A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N -mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in details have been tested numerically in a recent work.

      PubDate: 2017-09-20T17:10:15Z
      DOI: 10.1016/j.physd.2017.09.001
  • Agent-based model of the effect of globalization on inequality and class
    • Authors: Joep H.M. Evers; David Iron; Theodore Kolokolnikov; John Rumsey
      Abstract: Publication date: Available online 14 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Joep H.M. Evers, David Iron, Theodore Kolokolnikov, John Rumsey
      We consider a variant of the Bouchaud-Mézard model for wealth distribution in a society which incorporates the interaction radius between the agents, to model the extent of globalization in a society. The wealth distribution depends critically on the extent of this interaction. When interaction is relatively local, a small cluster of individuals emerges which accumulate most of the society’s wealth. In this regime, the society is highly stratified with little or no class mobility. As the interaction is increased, the number of wealthy agents decreases, but the overall inequality rises as the freed-up wealth is transferred to the remaining wealthy agents. However when the interaction exceeds a certain critical threshold, the society becomes highly mobile resulting in a much lower economic inequality (low Gini index). This is consistent with the Kuznets upside-down U shaped inequality curve hypothesis.

      PubDate: 2017-09-20T17:10:15Z
      DOI: 10.1016/j.physd.2017.08.009
  • The stability spectrum for elliptic solutions to the sine-Gordon equation
    • Authors: Bernard Deconinck; Peter McGill; Benjamin L. Segal
      Abstract: Publication date: Available online 14 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Bernard Deconinck, Peter McGill, Benjamin L. Segal
      We present an analysis of the stability spectrum for all stationary periodic solutions to the sine-Gordon equation. An analytical expression for the spectrum is given. From this expression, various quantitative and qualitative results about the spectrum are derived. Specifically, the solution parameter space is shown to be split into regions of distinct qualitative behavior of the spectrum, in one of which the solutions are stable. Additional results on the spectral stability of solutions with respect to perturbations of an integer multiple of the solution period are given.

      PubDate: 2017-09-14T16:57:02Z
      DOI: 10.1016/j.physd.2017.08.010
  • Chaotic dynamics of large-scale double-diffusive convection in a porous
    • Authors: Shutaro Kondo; Hiroshi Gotoda; Takaya Miyano; Isao T. Tokuda
      Abstract: Publication date: Available online 14 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Shutaro Kondo, Hiroshi Gotoda, Takaya Miyano, Isao T. Tokuda
      We have studied the chaotic dynamics of the large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan–Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.

      PubDate: 2017-09-14T16:57:02Z
      DOI: 10.1016/j.physd.2017.08.011
  • Multiple equilibria, bifurcations and selection scenarios in cosymmetric
           problem of thermal convection in porous medium
    • Authors: Vasily N. Govorukhin; Igor V. Shevchenko
      Abstract: Publication date: Available online 14 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Vasily N. Govorukhin, Igor V. Shevchenko
      We study convection in a two-dimensional container of porous material saturated with fluid and heated from below. This problem belongs to the class of dynamical systems with nontrivial cosymmetry. The cosymmetry gives rise to a hidden parameter in the system and continuous families of infinitely many equilibria, and leads to non-trivial bifurcations. In this article we present our numerical studies that demonstrate nonlinear phenomena resulting from the existence of cosymmetry. We give a comprehensive picture of different bifurcations which occur in cosymmetric dynamical systems and in the convection problem. It includes internal and external (as an invariant set) bifurcations of one-parameter families of equilibria, as well as bifurcations leading to periodic, quasiperiodic and chaotic behaviour. The existence of infinite number of stable steady-state regimes begs the important question as to which of them can realize in physical experiments. In the paper, this question (known as the selection problem) is studied in detail. In particular, we show that the selection scenarios strongly depend on the initial temperature distribution of the fluid. The calculations are carried out by the global cosymmetry-preserving Galerkin method, and numerical methods used to analyse cosymmetric systems are also described.

      PubDate: 2017-09-14T16:57:02Z
      DOI: 10.1016/j.physd.2017.08.012
  • Bounded ultra-elliptic solutions of the defocusing nonlinear
           Schrödinger equation
    • Authors: Otis C. Wright; III
      Abstract: Publication date: Available online 12 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Otis C. Wright III
      An effective integration method is presented for the bounded ultra-elliptic solutions of the defocusing nonlinear Schrödinger equation. The two-phase solutions are explicitly parametrized in terms of two physically-meaningful variables: the energy density and the momentum density. Cavitation, viz., a minimum amplitude of zero, occurs if and only if the length of the largest spectral band is less than or equal to the sum of the lengths of the two smaller spectral bands. In the case of strict inequality, there are exactly two cavitation points in each period parallelogram.

      PubDate: 2017-09-14T16:57:02Z
      DOI: 10.1016/j.physd.2017.08.013
  • A coherent structure approach for parameter estimation in Lagrangian Data
    • Authors: John Maclean; Naratip Santitissadeekorn; Christopher K.R.T. Jones
      Abstract: Publication date: Available online 5 September 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): John Maclean, Naratip Santitissadeekorn, Christopher K.R.T. Jones
      We introduce a data assimilation method to estimate model parameters with observations of passive tracers by directly assimilating Lagrangian Coherent Structures. Our approach differs from the usual Lagrangian Data Assimilation approach, where parameters are estimated based on tracer trajectories. We employ the Approximate Bayesian Computation (ABC) framework to avoid computing the likelihood function of the coherent structure, which is usually unavailable. We solve the ABC by a Sequential Monte Carlo (SMC) method, and use Principal Component Analysis (PCA) to identify the coherent patterns from tracer trajectory data. Our new method shows remarkably improved results compared to the bootstrap particle filter when the physical model exhibits chaotic advection.

      PubDate: 2017-09-09T06:52:08Z
      DOI: 10.1016/j.physd.2017.08.007
  • A classical limit-cycle system that mimics the quantum-mechanical harmonic
    • Authors: Yair Zarmi
      Abstract: Publication date: Available online 31 August 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Yair Zarmi
      Classical harmonic oscillators affected by appropriately chosen nonlinear dissipative perturbations can exhibit infinite sequences of limit cycles, which mimic quantized systems. For properly chosen perturbations, the large-amplitude limit cycles approach circles. The higher the amplitude of the limit cycle is, the smaller are the dissipative deviations from energy conservation. The weaker the perturbation is, the earlier on does the asymptotic behavior show up already in low-lying limit cycles. Simple modifications of the Rayleigh and van der Pol oscillators yield infinite sequences of limit cycles such that the energy spectrum of the higher-amplitude limit cycles tends to that of the quantum-mechanical particle in a box. For another judiciously chosen dissipative perturbation, the energy spectrum of the higher-amplitude limit cycles tends to that of the quantum-mechanical harmonic oscillator. In all cases, one first finds the limit-cycle solutions for dissipation strength, ε ≠ 0 . The “energy of each limit cycle” then oscillates around an average value. In the limit ε → 0 these oscillations vanish, and the limit cycles in the infinite sequence attain constant values for their energies, a characteristic that is required for such classical systems to mimic Hamiltonian quantum-mechanical systems.

      PubDate: 2017-09-02T22:27:45Z
      DOI: 10.1016/j.physd.2017.08.003
  • Dynamical systems analysis of the Maasch–Saltzman model for glacial
    • Authors: Hans Engler; Hans G. Kaper; Tasso J. Kaper; Theodore Vo
      Abstract: Publication date: Available online 24 August 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Hans Engler, Hans G. Kaper, Tasso J. Kaper, Theodore Vo
      This article is concerned with the internal dynamics of a conceptual model proposed by Maasch and Saltzman (1990) to explain central features of the glacial cycles observed in the climate record of the Pleistocene Epoch. It is shown that, in most parameter regimes, the long-term system dynamics occur on certain intrinsic two-dimensional invariant manifolds in the three-dimensional state space. These invariant manifolds are slow manifolds when the characteristic time scales for the total global ice mass and the strength of the North Atlantic Deep Water circulation are well-separated, and they are center manifolds when these characteristic time scales are comparable. In both cases, the reduced dynamics on these manifolds are governed by Bogdanov-Takens singularities, and the bifurcation curves associated to these singularities organize the parameter regions in which the model exhibits glacial cycles. In addition, knowledge of the reduced systems and their bifurcations is useful for understanding the effects slowly varying parameters, which cause passage through Hopf bifurcations, and of orbital (Milankovitch) forcing. Both are central to the mechanism proposed by Maasch and Saltzman for the mid-Pleistocene transition in their model.

      PubDate: 2017-09-02T22:27:45Z
      DOI: 10.1016/j.physd.2017.08.006
  • Vanishing viscosity limit for global attractors for the damped
           Navier–Stokes system with stress free boundary conditions
    • Authors: Vladimir Chepyzhov; Alexei Ilyin; Sergey Zelik
      Abstract: Publication date: Available online 23 August 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Vladimir Chepyzhov, Alexei Ilyin, Sergey Zelik
      We consider the damped and driven Navier–Stokes system with stress free boundary conditions and the damped Euler system in a bounded domain Ω ⊂ R 2 . We show that the damped Euler system has a (strong) global attractor in  H 1 ( Ω ) . We also show that in the vanishing viscosity limit the global attractors of the Navier–Stokes system converge in the non-symmetric Hausdorff distance in H 1 ( Ω ) to the strong global attractor of the limiting damped Euler system (whose solutions are not necessarily unique).

      PubDate: 2017-09-02T22:27:45Z
      DOI: 10.1016/j.physd.2017.08.005
  • Modeling and numerical investigations for hierarchical pattern formation
           in desiccation cracking
    • Authors: Sayako Hirobe; Kenji Oguni
      Abstract: Publication date: Available online 16 August 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Sayako Hirobe, Kenji Oguni
      Desiccation cracking and its pattern formation are widely observed in nature. The network of the surface cracks forms polygonal cells with typical size. This crack pattern is not formed in a simultaneous manner, instead, formed in a sequential and hierarchical manner. The strain energy accumulated by the heterogeneous drying shrinkage strain is systematically released by the cracks. In this sense, desiccation cracking phenomenon can be regarded as a typical example of the pattern formation in the dynamical system with dissipation. We propose a mathematical model for the pattern formation in desiccation cracking with emphasis on the emergence of the typical length scale with the typical geometry resulting from the hierarchical cell tessellation. The desiccation crack phenomenon is modeled as the coupling of desiccation, deformation, and fracture. This coupling model is numerically solved by weakly coupled analysis of the desiccation process and the deformation/fracture process. The basic features of the desiccation crack pattern and its formation process reproduced by the numerical analysis show reasonable agreement with experimental observations. This agreement implies that the proposed coupling model properly addresses the fundamental mechanism for the hierarchical pattern formation in desiccation cracking.

      PubDate: 2017-09-02T22:27:45Z
      DOI: 10.1016/j.physd.2017.08.002
  • Bifurcations of relative periodic orbits in NLS/GP with a triple-well
    • Authors: Roy H. Goodman
      Abstract: Publication date: Available online 5 August 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Roy H. Goodman
      The nonlinear Schrödinger/Gross–Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. The problem is reduced to a finite-dimensional Hamiltonian system by a Galerkin truncation. Families of oscillatory orbits are sought in the neighborhoods of the system’s nine branches of standing wave solutions. Normal forms are computed in the neighborhood of these branches’ various Hamiltonian Hopf and saddle–node bifurcations, showing how the oscillatory orbits change as a parameter is increased. Numerical experiments show agreement between normal form theory and numerical solutions to the reduced system and NLS/GP near the Hamiltonian Hopf bifurcations and some subtle disagreements near the saddle–node bifurcations due to exponentially small terms in the asymptotics.

      PubDate: 2017-09-02T22:27:45Z
      DOI: 10.1016/j.physd.2017.07.007
  • A modified hybrid Van der Pol–Duffing–Rayleigh oscillator for
           modelling the lateral walking force on a rigid floor
    • Authors: Prakash Kumar; Anil Kumar; Silvano Erlicher
      Abstract: Publication date: Available online 4 August 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Prakash Kumar, Anil Kumar, Silvano Erlicher
      The paper proposes a single degree of freedom oscillator in order to accurately represent the lateral force acting on a rigid floor due to human walking. As a pedestrian produces itself the energy required to maintain its motion, it can be modelled as a self-sustained oscillator that is able to produce: (i) self-sustained motion; (ii) a lateral periodic force signal; and (iii) a stable limit cycle. The proposed oscillator is a modification of hybrid Van der Pol–Duffing–Rayleigh oscillator, by introducing an additional nonlinear hardening term. Stability analysis of the proposed oscillator has been performed by using the energy balance method and the Lindstedt–Poincare perturbation technique. Model parameters were identified from the experimental force signals of ten pedestrians using the least squares identification technique. The experimental and the model generated lateral forces show a good agreement.

      PubDate: 2017-09-02T22:27:45Z
      DOI: 10.1016/j.physd.2017.07.008
  • Nanopteron solutions of diatomic Fermi-Pasta–Ulam-Tsingou lattices
           with small mass-ratio
    • Authors: Aaron Hoffman; J. Douglas Wright
      Abstract: Publication date: Available online 31 July 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Aaron Hoffman, J. Douglas Wright
      Consider an infinite chain of masses, each connected to its nearest neighbors by a (nonlinear) spring. This is a Fermi-Pasta–Ulam-Tsingou lattice. We prove the existence of traveling waves in the setting where the masses alternate in size. In particular we address the limit where the mass ratio tends to zero. The problem is inherently singular and we find that the traveling waves are not true solitary waves but rather “nanopterons”, which is to say, waves which asymptotic at spatial infinity to very small amplitude periodic waves. Moreover, we can only find solutions when the mass ratio lies in a certain open set. The difficulties in the problem all revolve around understanding Jost solutions of a nonlocal Schrödinger operator in its semi-classical limit.

      PubDate: 2017-08-03T21:43:26Z
      DOI: 10.1016/j.physd.2017.07.004
  • Emergence of unstable modes for classical shock waves in isothermal ideal
    • Authors: Heinrich Freistühler; Felix Kleber; Johannes Schropp
      Abstract: Publication date: Available online 31 July 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Heinrich Freistühler, Felix Kleber, Johannes Schropp
      This note studies classical magnetohydrodynamic shock waves in an inviscid fluidic plasma that is assumed to be a perfect conductor of heat as well as of electricity. For this mathematically prototypical material, it identifies, mainly numerically, two critical manifolds in parameter space, across which slow resp. fast MHD shock waves undergo emergence of a complex conjugate pair of unstable transverse modes. For slow shocks, this emergence occurs in a particularly interesting way already in the parallel case, in which it happens at the spectral value λ ˆ ≡ λ ∕ ω = 0 and the critical manifold possesses a simple explicit algebraic representation. Results of refined numerical treatment show that within the set of non-parallel slow shocks the unstable mode pair emerges from two generically different spectral values λ ˆ = ± i γ . For fast shocks, the critical manifold does not intersect the parallel regime and the emergence within the set of non-parallel fast shocks again starts from two generically different spectral values.

      PubDate: 2017-08-03T21:43:26Z
      DOI: 10.1016/j.physd.2017.07.005
  • Time-dependent spectral renormalization method
    • Authors: Justin T. Cole; Ziad H. Musslimani
      Abstract: Publication date: Available online 29 July 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Justin T. Cole, Ziad H. Musslimani
      The spectral renormalization method was introduced by Ablowitz and Musslimani (2005), as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel’s principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable P T symmetric nonlocal NLS and the viscous Burgers’ equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

      PubDate: 2017-08-03T21:43:26Z
      DOI: 10.1016/j.physd.2017.07.006
  • Boundary layer analysis for the stochastic nonlinear
           reaction–diffusion equations
    • Authors: Youngjoon Hong; Chang-Yeol Jung; Roger Temam
      Abstract: Publication date: Available online 29 July 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Youngjoon Hong, Chang-Yeol Jung, Roger Temam
      Singularly perturbed stochastic (and deterministic) nonlinear reaction–diffusion equations are considered. We first study the governing problem posed in the channel domain with lateral periodicity and extend the results to general smooth domains. Introducing corrector functions, which correct the boundary values discrepancies, we are able to develop the convergence analysis. For the analysis, we make use of the maximum principle to estimate the corrector functions. The stochastic problems also rely on the deterministic corrector functions, which lead to simpler computations than those of the stochastic version of the correctors.

      PubDate: 2017-08-03T21:43:26Z
      DOI: 10.1016/j.physd.2017.07.002
  • Multivariate Hadamard self-similarity: Testing fractal connectivity
    • Authors: Herwig Wendt; Gustavo Didier; Sébastien Combrexelle; Patrice Abry
      Abstract: Publication date: Available online 16 July 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Herwig Wendt, Gustavo Didier, Sébastien Combrexelle, Patrice Abry
      While scale invariance is commonly observed in each component of real world multivariate signals, it is also often the case that the inter-component correlation structure is not fractally connected, i.e., its scaling behavior is not determined by that of the individual components. To model this situation in a versatile manner, we introduce a class of multivariate Gaussian stochastic processes called Hadamard fractional Brownian motion (HfBm). Its theoretical study sheds light on the issues raised by the joint requirement of entry-wise scaling and departures from fractal connectivity. An asymptotically normal wavelet-based estimator for its scaling parameter, called the Hurst matrix, is proposed, as well as asymptotically valid confidence intervals. The latter are accompanied by original finite sample procedures for computing confidence intervals and testing fractal connectivity from one single and finite size observation. Monte Carlo simulation studies are used to assess the estimation performance as a function of the (finite) sample size, and to quantify the impact of omitting wavelet cross-correlation terms. The simulation studies are shown to validate the use of approximate confidence intervals, together with the significance level and power of the fractal connectivity test. The test performance and properties are further studied as functions of the HfBm parameters.

      PubDate: 2017-07-24T03:26:34Z
      DOI: 10.1016/j.physd.2017.07.001
  • Integrable U(1)-invariant peakon equations from the NLS hierarchy
    • Authors: Stephen C. Anco; Fatane Mobasheramini
      Abstract: Publication date: Available online 13 July 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Stephen C. Anco, Fatane Mobasheramini
      Two integrable U ( 1 ) -invariant peakon equations are derived from the NLS hierarchy through the tri-Hamiltonian splitting method. A Lax pair, a recursion operator, a bi-Hamiltonian formulation, and a hierarchy of symmetries and conservation laws are obtained for both peakon equations. These equations are also shown to arise as potential flows in the NLS hierarchy by applying the NLS recursion operator to flows generated by space translations and U ( 1 ) -phase rotations on a potential variable. Solutions for both equations are derived using a peakon ansatz combined with an oscillatory temporal phase. This yields the first known example of a peakon breather. Spatially periodic counterparts of these solutions are also obtained.

      PubDate: 2017-07-24T03:26:34Z
      DOI: 10.1016/j.physd.2017.06.006
  • Generic torus canards
    • Authors: Theodore
      Abstract: Publication date: Available online 4 July 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Theodore Vo
      Torus canards are special solutions of fast/slow systems that alternate between attracting and repelling manifolds of limit cycles of the fast subsystem. A relatively new dynamic phenomenon, torus canards have been found in neural applications to mediate the transition from tonic spiking to bursting via amplitude-modulated spiking. In R 3 , torus canards are degenerate: they require one-parameter families of 2-fast/1-slow systems in order to be observed and even then, they only occur on exponentially thin parameter intervals. The addition of a second slow variable unfolds the torus canard phenomenon, making it generic and robust. That is, torus canards in fast/slow systems with (at least) two slow variables occur on open parameter sets. So far, generic torus canards have only been studied numerically, and their behaviour has been inferred based on averaging and canard theory. This approach, however, has not been rigorously justified since the averaging method breaks down near a fold of periodics, which is exactly where torus canards originate. In this work, we combine techniques from Floquet theory, averaging theory, and geometric singular perturbation theory to show that the average of a torus canard is a folded singularity canard. In so doing, we devise an analytic scheme for the identification and topological classification of torus canards in fast/slow systems with two fast variables and k slow variables, for any positive integer k . We demonstrate the predictive power of our results in a model for intracellular calcium dynamics, where we explain the mechanisms underlying a novel class of elliptic bursting rhythms, called amplitude-modulated bursting, by constructing the torus canard analogues of mixed-mode oscillations. We also make explicit the connection between our results here with prior studies of torus canards and torus canard explosion in R 3 , and discuss how our methods can be extended to fast/slow systems of arbitrary (finite) dimension.

      PubDate: 2017-07-12T02:37:34Z
  • Dispersion managed solitons in the presence of saturated nonlinearity
    • Authors: Dirk Hundertmark; Young-Ran Lee; Tobias Ried; Vadim Zharnitsky
      Abstract: Publication date: Available online 29 June 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Dirk Hundertmark, Young-Ran Lee, Tobias Ried, Vadim Zharnitsky
      The averaged dispersion managed nonlinear Schrödinger equation with saturated nonlinearity is considered. It is shown that under rather general assumptions on the saturated nonlinearity, the ground state solution corresponding to the dispersion managed soliton can be found for both zero residual dispersion and positive residual dispersion. The same applies to diffraction management solitons, which are a discrete version describing certain waveguide arrays.

      PubDate: 2017-07-03T11:28:05Z
      DOI: 10.1016/j.physd.2017.06.004
  • Spatiotemporal algebraically localized waveforms for a nonlinear
           Schrödinger model with gain and loss
    • Authors: Z.A. Anastassi; G. Fotopoulos; D.J. Frantzeskakis; T.P. Horikis; N.I. Karachalios; P.G. Kevrekidis; I.G. Stratis; K. Vetas
      Abstract: Publication date: Available online 27 June 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Z.A. Anastassi, G. Fotopoulos, D.J. Frantzeskakis, T.P. Horikis, N.I. Karachalios, P.G. Kevrekidis, I.G. Stratis, K. Vetas
      We consider the asymptotic behavior of the solutions of a nonlinear Schrödinger (NLS) model incorporating linear and nonlinear gain/loss. First, we describe analytically the dynamical regimes (depending on the gain/loss strengths), for finite-time collapse, decay, and global existence of solutions in the dynamics. Then, for all the above parametric regimes, we use direct numerical simulations to study the dynamics corresponding to algebraically decaying initial data. We identify crucial differences between the dynamics of vanishing initial conditions, and those converging to a finite constant background: in the former (latter) case we find strong (weak) collapse or decay, when the gain/loss parameters are selected from the relevant regimes. One of our main results, is that in all the above regimes, non-vanishing initial data transition through spatiotemporal, algebraically decaying waveforms. While the system is nonintegrable, the evolution of these waveforms is reminiscent to the evolution of the Peregrine rogue wave of the integrable NLS limit. The parametric range of gain and loss for which this phenomenology persists is also touched upon.

      PubDate: 2017-07-03T11:28:05Z
      DOI: 10.1016/j.physd.2017.06.003
  • Overhanging of membranes and filaments adhering to periodic graph
    • Authors: Tatsuya Miura
      Abstract: Publication date: Available online 20 June 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Tatsuya Miura
      This paper mathematically studies membranes and filaments adhering to periodic patterned substrates in a one-dimensional model. The problem is formulated by the minimizing problem of an elastic energy with a contact potential on graph substrates. Global minimizers (ground states) are mainly considered in view of their graph representations. Our main results exhibit sufficient conditions for the graph representation and examples of situations where any global minimizer must overhang.

      PubDate: 2017-06-22T11:05:22Z
  • Distributed synaptic weights in a LIF neural network and learning rules
    • Authors: Benoî t Perthame; Delphine Salort; Gilles Wainrib
      Abstract: Publication date: Available online 15 June 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Benoî t Perthame, Delphine Salort, Gilles Wainrib
      Leaky integrate-and-fire (LIF) models are mean-field limits, with a large number of neurons, used to describe neural networks. We consider inhomogeneous networks structured by a connectivity parameter (strengths of the synaptic weights) with the effect of processing the input current with different intensities. We first study the properties of the network activity depending on the distribution of synaptic weights and in particular its discrimination capacity. Then, we consider simple learning rules and determine the synaptic weight distribution it generates. We outline the role of noise as a selection principle and the capacity to memorized a learned signal.

      PubDate: 2017-06-16T10:48:06Z
      DOI: 10.1016/j.physd.2017.05.005
  • Multi-model cross-pollination in time
    • Authors: Hailiang Du; Leonard A. Smith
      Abstract: Publication date: Available online 13 June 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Hailiang Du, Leonard A. Smith
      The predictive skill of complex models is rarely uniform in model-state space; in weather forecasting models, for example, the skill of the model can be greater in the regions of most interest to a particular operational agency than it is in “remote” regions of the globe. Given a collection of models, a multi-model forecast system using the cross-pollination in time approach can be generalized to take advantage of instances where some models produce forecasts with more information regarding specific components of the model-state than other models, systematically. This generalization is stated and then successfully demonstrated in a moderate ( ∼ 40 ) dimensional nonlinear dynamical system, suggested by Lorenz, using four imperfect models with similar global forecast skill. Applications to weather forecasting and in economic forecasting are discussed. Given that the relative importance of different phenomena in shaping the weather changes in latitude, changes in attitude among forecast centers in terms of the resources assigned to each phenomena are to be expected. The demonstration establishes that cross-pollinating elements of forecast trajectories enriches the collection of simulations upon which the forecast is built, and given the same collection of models can yield a new forecast system with significantly more skill than the original forecast system.

      PubDate: 2017-06-16T10:48:06Z
      DOI: 10.1016/j.physd.2017.06.001
  • Well-posedness and dynamics of a fractional stochastic
           integro-differential equation
    • Authors: Linfang Liu; Tomás Caraballo
      Abstract: Publication date: Available online 9 June 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Linfang Liu, Tomás Caraballo
      In this paper we investigate the well-posedness and dynamics of a fractional stochastic integro-differential equation describing a reaction process depending on the temperature itself. Existence and uniqueness of solutions of the integro-differential equation is proved by the Lumer–Phillips theorem. Besides, under appropriate assumptions on the memory kernel and on the magnitude of the nonlinearity, the existence of random attractor is achieved by obtaining first some a priori estimates. Moreover, the random attractor is shown to have finite Hausdorff dimension.

      PubDate: 2017-06-12T10:36:04Z
      DOI: 10.1016/j.physd.2017.05.006
  • Analysis of mixed-mode oscillation-incrementing bifurcations generated in
           a nonautonomous constrained Bonhoeffer–van der Pol oscillator
    • Authors: Takuji Kousaka; Yutsuki Ogura; Kuniyasu Shimizu; Hiroyuki Asahara; Naohiko Inaba
      Abstract: Publication date: Available online 1 June 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Takuji Kousaka, Yutsuki Ogura, Kuniyasu Shimizu, Hiroyuki Asahara, Naohiko Inaba
      Mixed-mode oscillations (MMOs) are phenomena observed in a number of dynamic settings, including electrical circuits and chemical systems. Mixed-mode oscillation-incrementing bifurcations (MMOIBs) are among the most complex MMO bifurcations observed in the large group of MMO-generating dynamics; however, only a few theoretical analyses of the mechanism causing MMOIBs have been performed to date. In this study, we use a degenerate technique to analyze MMOIBs generated in a Bonhoeffer-van der Pol oscillator with a diode under weak periodic perturbation. We consider the idealized case in which the diode operates as an ideal switch; in this case, the governing equation of the oscillator is a piecewise smooth constraint equation and the Poincaré return map is one-dimensional, and we find that MMOIBs occur in a manner similar to period-adding bifurcations generated by the circle map. Our numerical results suggest that the universal constant converges to 1.0 and our experimental results demonstrate that MMOIBs can occur successively many times. Our one-dimensional Poincaré return map clearly answers the fundamental question of why MMOs are related to Farey sequences even though each MMO-generating region in the parameter space is terminated by chaos.

      PubDate: 2017-06-02T09:28:10Z
      DOI: 10.1016/j.physd.2017.05.001
  • Averaging theory at any order for computing limit cycles of discontinuous
           piecewise differential systems with many zones
    • Authors: Jaume Llibre; Douglas D. Novaes; Camila A.B. Rodrigues
      Abstract: Publication date: Available online 24 May 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Jaume Llibre, Douglas D. Novaes, Camila A.B. Rodrigues
      This work is devoted to study the existence of periodic solutions for a class ε -family of discontinuous differential systems with many zones. We show that the averaged functions at any order control the existence of crossing limit cycles for systems in this class. We also provide some examples dealing with nonsmooth perturbations of nonlinear centers.

      PubDate: 2017-05-28T09:23:39Z
      DOI: 10.1016/j.physd.2017.05.003
  • The influence of canalization on the robustness of Boolean networks
    • Authors: C. Kadelka; J. Kuipers; R. Laubenbacher
      Abstract: Publication date: Available online 17 May 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): C. Kadelka, J. Kuipers, R. Laubenbacher
      Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on networks governed by k -canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The variable activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to c -sensitivity and provides formulas for the activities and c -sensitivity of general k -canalizing functions as well as canalizing functions with more precisely defined structure. A popular measure for the robustness of a network, the Derrida value, can be expressed as a weighted sum of the c -sensitivities of the governing canalizing functions, and can also be calculated for a stochastic extension of Boolean networks. These findings provide a computationally efficient way to obtain Derrida values of Boolean networks, deterministic or stochastic, that does not involve simulation.

      PubDate: 2017-05-23T09:10:50Z
      DOI: 10.1016/j.physd.2017.05.002
  • Optimal strategies for the control of autonomous vehicles in data
    • Authors: D. McDougall; R.O. Moore
      Abstract: Publication date: Available online 5 May 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): D. McDougall, R.O. Moore
      We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for the locally optimal control algorithm presented here, with objective formed from the variance trace of the expected posterior distribution. We present results for linear flows near hyperbolic fixed points.

      PubDate: 2017-05-07T15:23:30Z
      DOI: 10.1016/j.physd.2017.04.001
  • Solution landscapes in nematic microfluidics
    • Authors: M. Crespo; A. Majumdar; A.M. Ramos; I.M. Griffiths
      Abstract: Publication date: Available online 4 May 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): M. Crespo, A. Majumdar, A.M. Ramos, I.M. Griffiths
      We study the static equilibria of a simplified Leslie–Ericksen model for a unidirectional uniaxial nematic flow in a prototype microfluidic channel, as a function of the pressure gradient G and inverse anchoring strength, B . We numerically find multiple static equilibria for admissible pairs ( G , B ) and classify them according to their winding numbers and stability. The case G = 0 is analytically tractable and we numerically study how the solution landscape is transformed as G increases. We study the one-dimensional dynamical model, the sensitivity of the dynamic solutions to initial conditions and the rate of change of G and B . We provide a physically interesting example of how the time delay between the applications of G and B can determine the selection of the final steady state.

      PubDate: 2017-05-07T15:23:30Z
      DOI: 10.1016/j.physd.2017.04.004
  • Invariant manifolds and the parameterization method in coupled energy
           harvesting piezoelectric oscillators
    • Authors: Albert Granados
      Abstract: Publication date: Available online 19 April 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Albert Granados
      Energy harvesting systems based on oscillators aim to capture energy from mechanical oscillations and convert it into electrical energy. Widely extended are those based on piezoelectric materials, whose dynamics are Hamiltonian submitted to different sources of dissipation: damping and coupling. These dissipations bring the system to low energy regimes, which is not desired in long term as it diminishes the absorbed energy. To avoid or to minimize such situations, we propose that the coupling of two oscillators could benefit from theory of Arnold diffusion. Such phenomenon studies O ( 1 ) energy variations in Hamiltonian systems and hence could be very useful in energy harvesting applications. This article is a first step towards this goal. We consider two piezoelectric beams submitted to a small forcing and coupled through an electric circuit. By considering the coupling, damping and forcing as perturbations, we prove that the unperturbed system possesses a 4-dimensional Normally Hyperbolic Invariant Manifold with 5 and 4-dimensional stable and unstable manifolds, respectively. These are locally unique after the perturbation. By means of the parameterization method, we numerically compute parameterizations of the perturbed manifold, its stable and unstable manifolds and study its inner dynamics. We show evidence of homoclinic connections when the perturbation is switched on.

      PubDate: 2017-04-25T10:34:15Z
      DOI: 10.1016/j.physd.2017.04.003
  • The spectrum of the torus profile to a geometric variational problem with
           long range interaction
    • Authors: Xiaofeng Ren; Juncheng Wei
      Abstract: Publication date: Available online 18 April 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Xiaofeng Ren, Juncheng Wei
      The profile problem for the Ohta-Kawasaki diblock copolymer theory is a geometric variational problem. The energy functional is defined on sets in R 3 of prescribed volume and the energy of an admissible set is its perimeter plus a long range interaction term related to the Newtonian potential of the set. This problem admits a solution, called a torus profile, that is a set enclosed by an approximate torus of the major radius 1 and the minor radius q . The torus profile is both axially symmetric about the z axis and reflexively symmetric about the x y -plane. There is a way to set up the profile problem in a function space as a partial differential-integro equation. The linearized operator L of the problem at the torus profile is decomposed into a family of linear ordinary differential-integro operators L m where the index m = 0 , 1 , 2 , . . . is called a mode. The spectrum of L is the union of the spectra of the L m ’s. It is proved that for each m , when q is sufficiently small, L m is positive definite. ( 0 is an eigenvalue for both L 0 and L 1 , due to the translation and rotation invariance.) As q tends to 0 , more and more L m ’s become positive definite. However no matter how small q is, there is always a mode m of which L m has a negative eigenvalue. This mode grows to infinity like q − 3 / 4 as q → 0 .

      PubDate: 2017-04-25T10:34:15Z
      DOI: 10.1016/j.physd.2017.01.001
  • Dynamical and energetic instabilities of F=2 spinor Bose-Einstein
           condensates in an optical lattice
    • Authors: Deng-Shan Wang; Yu-Ren Shi; Wen-Xing Feng; Lin Wen
      Abstract: Publication date: Available online 17 April 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Deng-Shan Wang, Yu-Ren Shi, Wen-Xing Feng, Lin Wen
      The dynamical and energetic instabilities of the F =2 spinor Bose-Einstein condensates in an optical lattice are investigated theoretically and numerically. By analyzing the dynamical response of different carrier waves to an additional linear perturbation, we obtain the instability criteria for the ferromagnetic, uniaxial nematic, biaxial nematic and cyclic states, respectively. When an external magnetic field is taken into account, we find that the linear or quadratic Zeeman effects obviously affect the dynamical instability properties of uniaxial nematic, biaxial nematic and cyclic states, but not for the ferromagnetic one. In particular, it is found that the faster moving F =2 spinor BEC has a larger energetic instability region than lower one in all the four states. In addition, it is seen that for most states there probably exists a critical value k c > 0 , for which k > k c gives the energetic instability to arise under appreciative parameters.

      PubDate: 2017-04-18T03:43:03Z
      DOI: 10.1016/j.physd.2017.04.002
  • On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled
    • Authors: A.S. Gonchenko; S.V. Gonchenko; A.O. Kazakov; D.V. Turaev
      Abstract: Publication date: Available online 30 March 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): A.S. Gonchenko, S.V. Gonchenko, A.O. Kazakov, D.V. Turaev
      A one-parameter family of time-reversible systems on three-dimensional torus is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the so-called mixed dynamics phenomenon which corresponds to a persistent intersection of the closure of the stable periodic orbits and the closure of the completely unstable periodic orbits. We search for the stable and unstable periodic orbits indirectly, by finding non-conservative saddle periodic orbits and heteroclinic connections between them. In this way, we are able to claim the existence of mixed dynamics for a large range of parameter values. We investigate local and global bifurcations that can be used for the detection of mixed dynamics.

      PubDate: 2017-04-04T03:13:49Z
      DOI: 10.1016/j.physd.2017.02.002
  • Pattern formation on the free surface of a ferrofluid: Spatial dynamics
           and homoclinic bifurcation
    • Authors: M.D. Groves; D.J.B. Lloyd; A. Stylianou
      Abstract: Publication date: Available online 23 March 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): M.D. Groves, D.J.B. Lloyd, A. Stylianou
      We establish the existence of spatially localised one-dimensional free surfaces of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisation law. It is shown that the ferrohydrostatic equations can be derived from a variational principle that allows one to formulate them as an (infinite-dimensional) spatial Hamiltonian system in which the unbounded free-surface direction plays the role of time. A centre-manifold reduction technique converts the problem for small solutions near onset to an equivalent Hamiltonian system with finitely many degrees of freedom. Normal-form theory yields the existence of homoclinic solutions to the reduced system, which correspond to spatially localised solutions of the ferrohydrostatic equations.

      PubDate: 2017-03-28T02:42:26Z
      DOI: 10.1016/j.physd.2017.03.004
  • Integrable systems and invariant curve flows in symplectic Grassmannian
    • Authors: Junfeng Song; Changzheng Qu; Ruoxia Yao
      Abstract: Publication date: Available online 21 March 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Junfeng Song, Changzheng Qu, Ruoxia Yao
      In this paper, local geometry of curves in the symplectic Grassmannian homogeneous space Sp ( 4 , R ) / ( Sp ( 2 , R ) × Sp ( 2 , R ) ) and its connection with that of the pseudo-hyperbolic space H 2 , 2 are studied. The group-based Serret-Frenet equations and the associated Maurer-Cartan differential invariants for the Grassmannian curves are obtained by using the equivariant moving frame method. The Grassmannian natural frame are also constructed by a gauge transformation from the Serret-Frenet frame, relating to the hyperbolic natural frame by the local Lie group isomorphism. Using the natural frames, invariant curve flows in the Grassmannian and the hyperbolic spaces are studied. It is shown that certain intrinsic curve flows induce the bi-Hamiltonian integrable matrix mKdV equation on the Maurer-Cartan differential invariants.

      PubDate: 2017-03-28T02:42:26Z
      DOI: 10.1016/j.physd.2017.02.013
  • Markovian properties of velocity increments in boundary layer turbulence
    • Authors: Murat Tutkun
      Abstract: Publication date: Available online 16 March 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Murat Tutkun
      Markovian properties of the turbulent velocity increments in a flat plate boundary layer at Re θ = 19100 are investigated using hot-wire anemometry measurements of the streamwise velocity component in a wind tunnel. Increments of the longitudinal velocities at different wall-normal positions show that the flow exhibits Markovian properties when the separation between different scales, or the Markov-Einstein coherence length, is on the order of the Taylor microscale, λ . The results indicate that Markovian nature of turbulence evolves across the boundary layer showing certain characteristics pertaining to the distance to the wall. The connection between the Markovian properties of turbulent boundary layer and existence of the spectral gap is explored. Markovianity of the process is also discussed in relation to the nonlocal nonlinear versus local nonlinear transfer of energy, triadic interactions and dissipation.

      PubDate: 2017-03-20T19:31:07Z
      DOI: 10.1016/j.physd.2017.03.002
  • Targeted energy transfer in laminar vortex-induced vibration of a sprung
           cylinder with a nonlinear dissipative rotator
    • Authors: Antoine Blanchard; Lawrence A. Bergman; Alexander F. Vakakis
      Abstract: Publication date: Available online 16 March 2017
      Source:Physica D: Nonlinear Phenomena
      Author(s): Antoine Blanchard, Lawrence A. Bergman, Alexander F. Vakakis
      We computationally investigate the dynamics of a linearly-sprung circular cylinder immersed in an incompressible flow and undergoing transverse vortex-induced vibration (VIV), to which is attached a rotational nonlinear energy sink (NES) consisting of a mass that freely rotates at constant radius about the cylinder axis, and whose motion is restrained by a rotational linear viscous damper. The inertial coupling between the rotational motion of the attached mass and the rectilinear motion of the cylinder is “essentially nonlinear”, which, in conjunction with dissipation, allows for one-way, nearly irreversible targeted energy transfer (TET) from the oscillating cylinder to the nonlinear dissipative attachment. At the intermediate Reynolds number R e = 100 , the NES-equipped sprung cylinder undergoes repetitive cycles of slowly decaying oscillations punctuated by intervals of chaotic instabilities. During the slowly decaying portion of each cycle, the dynamics of the cylinder is regular and, for large enough values of the ratio ε of the NES mass to the total mass (i.e., NES mass plus cylinder mass), can lead to significant vortex street elongation with partial stabilization of the wake. As ε approaches zero, no such vortex elongation is observed and the wake patterns appear similar to that for a sprung cylinder with no NES. We apply proper orthogonal decomposition (POD) to the velocity flow field during a slowly decaying portion of the solution and show that, in situations where vortex elongation occurs, the NES, though not in direct contact with the surrounding fluid, has a drastic effect on the underlying flow structures, imparting significant and continuous passive redistribution of energy among POD modes. We construct a POD-based reduced-order model for the lift coefficient to characterize energy transactions between the fluid and the cylinder throughout the slowly decaying cycle. We introduce a quantitative signed measure of the work done by the fluid on the cylinder over one quasi-period of the slowly decaying response and find that vortex elongation is associated with a sign change of that measure, indicating that a reversal of the direction of energy transfer, with the cylinder “leaking energy back” to the flow, is responsible for partial stabilization and elongation of the wake. We interpret these findings in terms of the spatial structure and energy distribution of the POD modes, and relate them to the mechanism of transient resonance capture into a slow invariant manifold of the fluid–structure interaction dynamics.

      PubDate: 2017-03-20T19:31:07Z
      DOI: 10.1016/j.physd.2017.03.003
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